1
VITEEE 2023
+1
-0

Let $$A$$ and $$B$$ be two independent events such that the odds in favour of $$A$$ and $$B$$ are $$1: 1$$ and $$3: 2$$, respectively. Then, the probability that only one of the two occurs is

A
0.6
B
0.8
C
0.5
D
0.4
2
VITEEE 2022
+1
-0

Two dices are rolled. If both dices have six faces numbered $$1,2,3,5,7$$ and $$11$$ then the probability that the sum of the number on the top faces is less than or equal to 8 is

A
$$\frac{4}{9}$$
B
$$\frac{17}{36}$$
C
$$\frac{5}{12}$$
D
$$\frac{1}{2}$$
3
VITEEE 2021
+1
-0

A bag contains 50 tickets numbered $$1,2,3, ..., 50$$ of which five are drawn at random and arranged in ascending order of magnitude $$\left(x_1 < x_2 < x_3 < x_4< x_5\right)$$, then the probability that $x_3=30$ is

A
$$\frac{{ }^{29} \mathrm{C}_2 \times{ }^{20} \mathrm{C}_2}{{ }^{50} \mathrm{C}_5}$$
B
$$\frac{{ }^{30} C_1 \times{ }^{29} C_1}{{ }^{50} C_5}$$
C
$$\frac{{ }^5 C_1 \times{ }^{50} C_2}{{ }^{50} C_5}$$
D
$$\frac{{ }^{50} C_2 \times{ }^{29} C_1}{{ }^{50} C_5}$$
4
VITEEE 2021
+1
-0

Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is

A
$$\frac{{ }^7 P_5}{7^5}$$
B
$$\frac{7^5}{{ }^7 P_5}$$
C
$$\frac{6}{{ }^6 P_5}$$
D
$$\frac{{ }^5 P_5}{5^5}$$
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